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### Messages - Shachi

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1
##### Partnership / Re: Partnership
« on: June 26, 2014, 05:00:45 AM »
We calculating the ratio for 12 months
A's contribution= 50000*12
since B left x months before the end of the year so his contribution=60000(12-x)
and same for C= 70000(12-x)
their ratios
50000*12:60000(12-x):70000(12-x)
=>    60  : 6(12-x)   : 7(12-x)
Now given ratio is 20:18:21
so we divide by 3 in the ratio
=>    20  : 3(12-x)   : 7(12-x)/3
on comparing the B's ratio with the given one we get
3(12-x)=18
x=3

2
##### Time and Work / Re: Time and Work Problem
« on: June 24, 2014, 05:07:34 AM »
if A and B works together then they complete the work in 12 days

1/A+1/B=1/12------>(eqn 1)

if B and C works together then they complete the work in 20/3 days

1/B+1/C=3/20------>(eqn 2)
Now,
A works for 3 days and B works for 4 days and C works for 7 days so the equation for this

3/A+4/B+7/C=1

Substitute the value of 1/A and 1/C  from equation 1 and 2 then we get,
3(1/12-1/B)+4/B+7(3/20-1/B)=1
1/B=1/20
now put 1/B=1/20 in equation 1 so we get,
1/A=1/30
that means A alone can complete the work in 30 days.

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